How to find the coordinates of the turning points of a curve on a graph

The turning point of a curve occurs when the gradient of the line = 0The differential equation (dy/dx) equals the gradient of a line. Therefore in this case the differential equation will equal 0.dy/dx = 0Let's work through an example. If the equation of a line = y =x+2xTherefore the differential equation will equaldy/dx = 2x +2therefore because dy/dx = 0 at the turning point then2x+2 = 0Therefore:2x+2 = 02x= -2x=-1 This is the x- coordinate of the turning pointYou can then sub this into the main equation (y=x2+2x) to find the y-coordinate. So if x = -1:y = (-1)2+2(-1)y = (1) +( - 2)y = 3This is the y-coordinate of the turning pointTherefore the coordinates of the turning point are x=-1, y =3= (-1,3)

CG
Answered by Charlotte G. Maths tutor

96332 Views

See similar Maths GCSE tutors

Related Maths GCSE answers

All answers ▸

What is the difference between LCM and HCF?


How do you translate the graph y = x^2, five unit squares negatively horizontally and 3 unit squares positively vertically?


Sean wants to go on holiday. He is going to get a loan of £ 720 to help pay for the holiday. Sean will have to pay back the £ 720 plus interest of 15 %. He will pay this back in 12 equal monthly installments. How much money will Sean pay back each month?


Solve this pair of simultaneous equations: 3x + 2y = 4 and 2x + y = 3


We're here to help

contact us iconContact ustelephone icon+44 (0) 203 773 6020
Facebook logoInstagram logoLinkedIn logo

© MyTutorWeb Ltd 2013–2025

Terms & Conditions|Privacy Policy
Cookie Preferences